Topological pseudo entropy

Nishioka, Tatsuma; Takayanagi, Tadashi; Taki, Yusuke

doi:10.1007/jhep09(2021)015

Cited by 35 publications

(16 citation statements)

References 62 publications

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“…There are several applications of pseudo entropy in literature. One can use the pseudo entropy as a diagnosis of whether two states belong to the same quantum phase or not [16][17][18]. The entanglement entropy for non-Hermitian systems [19] can be understood as a concrete example of pseudo entropy as the left and right energy eigenstates are different in non-Hermitian Hamiltonians.…”

Section: S(τmentioning

confidence: 99%

Notes on Pseudo Entropy Amplification

Ishiyama¹,

Kojima²,

Matsui³

et al. 2022

Preprint

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We study pseudo entropy for a particular linear combination of entangled states in qubit systems, two-dimensional free conformal field theories (CFT), and two-dimensional holographic CFT. We observe phenomena that the pseudo entropy can be parametrically large compared with the logarithm of the dimension of Hilbert space. We call these phenomena pseudo entropy amplification. The pseudo entropy amplification is analogous to the amplification of the weak value. In particular, our result suggests the holographic CFT does not lead the amplification as long as the non-perturbative effects are negligible. We also give a heuristic argument when such (non-)amplification can occur.

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Section: S(τmentioning

confidence: 99%

Notes on Pseudo Entropy Amplification

Ishiyama¹,

Kojima²,

Matsui³

et al. 2022

Preprint

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“…Otherwise, it will be computing pseudo entropy in general. For example, pseudo entropies are computed by considering non symmetric Euclidean path integrals in [50,[61][62][63].…”

Section: B1 Euclidean Path Integrals and Reflection Symmetriesmentioning

confidence: 99%

Zoo of holographic moving mirrors

Akal,

Kawamoto,

Ruan

et al. 2022

Preprint

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We systematically study moving mirror models in two-dimensional conformal field theory (CFT). By focusing on their late-time behavior, we separate the mirror profiles into four classes, named type A (timelike) mirrors, type B (escaping) mirrors, type C (chasing) mirrors, and type D (terminated) mirrors. We analytically explore the characteristic features of the energy flux and entanglement entropy for each type and work out their physical interpretation. Moreover, we construct their gravity duals for which end-of-the-world (EOW) branes play a crucial role. Depending on the mirror type, the profiles of the EOW branes show distinct behaviors. In addition, we also provide a criterion that decides whether the replica method in CFTs computes entanglement entropy or pseudo entropy in moving mirror models.

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“…A main claim we will advocate in this paper is the pseudo entanglement wedge reconstruction does fill this gap and offers a natural interpretation of entanglement wedge reconstruction in such situations. The pseudo entanglement wedge reconstruction is a natural generalization of entanglement wedge reconstruction for the bulk transition matrix which is defined on a subregion of a bulk timeslice, whose boundary is the extremal surface for the pseudo entropy [96][97][98][99]. The pseudo entropy is a natural generalization of von Neumann entropy of transition matrix, whose value can be complex.…”

Section: Jhep12(2021)013mentioning

confidence: 99%

Island for gravitationally prepared state and pseudo entanglement wedge

Miyaji

2021

J. High Energ. Phys.

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We consider spacetime initiated by a finite-sized initial boundary as a generalization of the Hartle-Hawking no-boundary state. We study entanglement entropy of matter state prepared by such spacetime. We find that the entanglement entropy for large subregion is given either by the initial state entanglement or the entanglement island, preventing the entropy to grow arbitrarily large. Consequently, the entanglement entropy is always bounded from above by the boundary area of the island, leading to an entropy bound in terms of the island. The island I is located in the analytically continued spacetime, either at the bra or the ket part of the spacetime in Schwinger-Keldysh formalism. The entanglement entropy is given by an average of complex pseudo generalized entropy for each entanglement island. We find a necessary condition of the initial state to be consistent with the strong sub-additivity, which requires that any probe degrees of freedom are thermally entangled with the rest of the system. We then find a large parameter region where the spacetime with finite-sized initial boundary, which does not have the factorization puzzle at leading order, dominates over the Hartle-Hawking no-boundary state or the bra-ket wormhole. Due to the absence of a moment of time reflection symmetry, the island in our setup is a generalization of the entanglement wedge, called pseudo entanglement wedge. In pseudo entanglement wedge reconstruction, we consider reconstructing the bulk matter transition matrix on A ∪ I, from a fine-grained state on A. The bulk transition matrix is given by a thermofield double state with a projection by the initial state. We also provide an AdS/BCFT model by considering EOW branes with corners. We also find the exponential hardness of such reconstruction task using a generalization of Python’s lunch conjecture to pseudo generalized entropy.

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Topological pseudo entropy

Cited by 35 publications

References 62 publications

Notes on Pseudo Entropy Amplification

Notes on Pseudo Entropy Amplification

Zoo of holographic moving mirrors

Island for gravitationally prepared state and pseudo entanglement wedge

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